What are some good books for self-studying mathematics, including number theory?

[nonick]

coming back to Mathematics!

hey

Its been long since i have done formal mathematics. I was good at mathematics at college and liked it as well. But ofcourse my skills have gone rusty. Now I want to study mathematics on my own, reading the high school mathematics (trignometry, algebra etc i.e basis of subjects) in depth with application. Would you please recommend some good books. Some people say that i should go with the Schaum Series. I have used those books for some quick recap at the grad school. What do you say? Please recommend some good books.

I wanted to read number theory actually but then i thought giving a good depth read to the basis is better. Can i start with the number theory right away?

many thanks

regards

 

[jbunniii]

Are you sure you really need to do a full review of high school mathematics if you've already learned it once? You might find that you remember more than you think, once you start trying to use it again.

It might be more efficient (and more motivating) to proceed with your actual goal, namely get an elementary number theory book and start reading it. Then when you get stuck, you can go back and review (or ask questions here!) just enough to get unstuck.

One book you might consider is

https://www.amazon.com/dp/3540761977/?tag=pfamazon01-20

It is pretty basic as number theory books go, and it includes solutions to all the exercises. You can preview it on Amazon to see whether it's over your head or not.

 

[kuahji]

I keep posting this list whenever I see these threads.

That should pretty much covered undergraduate subjects, depending on what you want to specialize in, & you certainly don't have to start from the beginning, but I think they are all really useful references. The Schaum's outline series is excellent as well, lots of example problems with solutions.

 

[nonick]

hey

many thanks for your replies and suggestions!

I didnt want to read everything of course:) i just wanted to say that i wanted to read mathematics in more depth. I think coz i have stayed away for so long so i am not confident enough. But thanks for the books suggestions. I think i will start with the Number theory right away

thanks

 

[qspeechc]

Well, if you feel you ability to do proofs has gone rusty too then I suggest you fix that first. A nice, gentle introduction to proofs is given by Principles of Mathematics by Allendoerfer and Oakley, which mixes high school mathematics and elementary university stuff, but does it rigorously. Some of the chapters you can skip if you feel you know the material well. The chapters on Probability and Boolean Algebra are only if you're interested, and I would say skim or skip or read thoroughly (depending on how well you know the stuff) the chapters on Equations and Inequalities, Exponential and Logarithmic Functions, and Trig Functions. All the other chapters are essential reading.
Actually I feel it is a very good idea to start with this book for two reasons: to refresh your knowledge of high school math; and to bring you up to speed on doing proofs.